Problem: A few families took a trip to an amusement park together. Tickets cost $$8.00$ each for adults and $$4.50$ each for kids, and the group paid $$51.00$ in total. There were $3$ fewer adults than kids in the group. Find the number of adults and kids on the trip.
Answer: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${8x+4.5y = 51}$ ${x = y-3}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-3}$ for $x$ in the first equation. ${8}{(y-3)}{+ 4.5y = 51}$ Simplify and solve for $y$ $ 8y-24 + 4.5y = 51 $ $ 12.5y-24 = 51 $ $ 12.5y = 75 $ $ y = \dfrac{75}{12.5} $ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into ${x = y-3}$ to find $x$ ${x = }{(6)}{ - 3}$ ${x = 3}$ You can also plug ${y = 6}$ into ${8x+4.5y = 51}$ and get the same answer for $x$ ${8x + 4.5}{(6)}{= 51}$ ${x = 3}$ There were $3$ adults and $6$ kids.